Let G be a graph in which each vertex has been coloured using one of k colours, Say c(1), c(2), - c(k). If an m-cycle C in G has ni vertices coloured c(i), i = 1, 2,., k, and vertical bar n(i) - n(j)vertical bar <= 1 for any i, j is an element of {1, 2,..., k}, then C is equitably k-coloured. An m-cycle decomposition C of a graph G is equitably k-colourabte if the vertices of G can be coloured so that every m-cycle in C is equitably k-coloured. For m = 4, 5 and 6, we completely settle the existence problem for equitably 2-colourable m-cycle decompositions of complete graphs and complete graphs with the edges of a I-factor removed.